Suppose we have a map of diagrams $X \to Y$ of shape $D$ in the category of sets. Suppose further this is an objectwise surjection. That is, $X_d \to Y_d$ is a surjection for all $d \in D$. Are there reasonable conditions where one can conclude that $\lim_DX \to \lim_DY$ is also a surjection? Particularly, any conditions on the diagram $D$ that would guarantee a surjection on the limits?
2026-03-26 01:26:27.1774488387
Surjection on limits
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